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A353962 Square array read by descending antidiagonals: The n-th row gives the decimal expansion of the base-n Champernowne constant.

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%I A353962 #54 Dec 26 2024 21:43:55
%S A353962 8,6,5,2,9,4,2,8,2,3,4,9,6,1,2,0,5,1,0,3,1,1,8,1,7,9,9,1,2,1,1,3,8,4,
%T A353962 6,1,5,6,1,6,6,4,3,4,1,8,7,1,1,2,3,2,0,2,1,6,5,1,1,6,5,6,6,3,0,0,8,3,
%U A353962 1,1,8,5,4,2,4,9,9,0,0,8,1,1,5,3,8,4,5,9,9,9,0
%N A353962 Square array read by descending antidiagonals: The n-th row gives the decimal expansion of the base-n Champernowne constant.
%C A353962 The base-n Champernowne constant (C_n) is normal in base n. A(n,k) is the (k+1)-th decimal digit of the fractional part of C_n.
%H A353962 Verónica Becher and Santiago Figueira, <a href="https://doi.org/10.1016/S0304-3975(01)00170-0">An example of a computable absolutely normal number</a>, Theoretical Computer Science, 270 (2002), 947-958.
%H A353962 Arthur H. Copeland and Paul Erdős, <a href="https://doi.org/10.1090/S0002-9904-1946-08657-7">Note on normal numbers</a>, Bull. Amer. Math. Soc. 52 (1946), 857-860.
%H A353962 Davar Khoshnevisan, <a href="https://www.claymath.org/library/annual_report/ar2006/06report_normalnumbers.pdf">Normal Numbers are Normal</a>, Clay Mathematics Institute Annual Report, 2006, 15-31.
%H A353962 Ivan Niven and H.S. Zuckerman, <a href="https://msp.org/pjm/1951/1-1/pjm-v1-n1-s.pdf#page=105">On The Definition of Normal Numbers</a>, Pacific J. Math., 1 (1951), 103-109.
%H A353962 Davis Smith, <a href="/A353962/a353962_3.txt">A Sufficient Condition For Normalcy.</a>
%F A353962 A(n,k) = floor(C_n*10^(k+1)) mod 10 where C_n (the base-n Champernowne constant) = Sum_{i>=1} i/(n^(i + Sum_{k=1..i-1} floor(log_n(k+1)))).
%e A353962 The square array A(n,k) begins:
%e A353962   n/k | 0  1  2  3  4  5  6  7  8  9 10 11 ...
%e A353962   ----+---------------------------------------
%e A353962    2  | 8  6  2  2  4  0  1  2  5  8  6  8 ...
%e A353962    3  | 5  9  8  9  5  8  1  6  7  5  3  8 ...
%e A353962    4  | 4  2  6  1  1  1  1  1  1  1  1  1 ...
%e A353962    5  | 3  1  0  7  3  6  1  1  1  1  1  1 ...
%e A353962    6  | 2  3  9  8  6  2  6  8  5  8  1  5 ...
%e A353962    7  | 1  9  4  4  3  5  5  3  5  0  8  6 ...
%e A353962    8  | 1  6  3  2  6  4  8  1  2  1  0  5 ...
%e A353962    9  | 1  4  0  6  2  4  9  7  6  1  1  9 ...
%e A353962   10  | 1  2  3  4  5  6  7  8  9  1  0  1 ...
%e A353962   ...
%t A353962 A[n_,k_]:=Mod[Floor[ChampernowneNumber[n]10^(k + 1)] ,10]; Flatten[Table[Reverse[Table[A[n-k,k],{k,0,n-2}]],{n,2,14}]] (* _Stefano Spezia_, May 13 2022 *)
%Y A353962 Rows: A066716 (n=2), A077771 (n=3), A033307 (n=10).
%Y A353962 Cf. A063945.
%K A353962 nonn,base,tabl
%O A353962 2,1
%A A353962 _Davis Smith_, May 12 2022